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We investigate the possibility of a strongly correlated Fractional QuantumHall (FQH) state in bulk three dimensional isotropic (not layered) materials.We find that a FQH state can exist at low densities only if it is accompaniedby a staging transition in which the electrons re-organize themselves inlayers, perpendicular to the magnetic field, at distances of order the magneticlength apart. The Hartree energy associated to the staging transition isoff-set by the correlation Fock energy of the 3D FQH state. We obtain the phasediagram of bulk electrons in a magnetic field subject to Coulomb interactionsas a function of carrier density and lattice constant. At very low densities,the 3D FQH state exhibits a transition to a 3D Wigner crystal state stabilizedby phonon correlations.

Scenario for Fractional Quantum Hall Effect in Bulk Isotropic Materials